A school is ordering T-shirts from two suppliers. From Supplier 1, 15% of the T-shirts are size Small, and from...

1. TRANSLATE the supplier information into mathematical expressions

• Given information:
  • Supplier 1: 15% of x T-shirts are Small
  • Supplier 2: 55% of y T-shirts are Small

• What this tells us:
  • Small T-shirts from Supplier 1: \(0.15\mathrm{x}\)
  • Small T-shirts from Supplier 2: \(0.55\mathrm{y}\)
  • Total Small T-shirts: \(0.15\mathrm{x} + 0.55\mathrm{y}\)

2. TRANSLATE the constraint into an inequality

• The phrase "no more than 260" means the total cannot exceed 260
• This translates to: \(\leq 260\)

3. Combine the expressions to form the complete inequality

• Total Small T-shirts \(\leq 260\)
• \(0.15\mathrm{x} + 0.55\mathrm{y} \leq 260\)

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students treat percentages as whole numbers instead of decimals.

Instead of converting 15% to 0.15, they use 15 directly, leading to the expression \(15\mathrm{x} + 55\mathrm{y} \leq 260\). This creates unrealistically large numbers since they're now counting 15 Small T-shirts for every 1 T-shirt ordered from Supplier 1.

This may lead them to select Choice D (\(15\mathrm{x} + 55\mathrm{y} \leq 260\))

Second Most Common Error:

Poor TRANSLATE reasoning: Students mix up which supplier has which percentage.

They correctly convert to decimals but assign 55% to Supplier 1 and 15% to Supplier 2, creating \(0.55\mathrm{x} + 0.15\mathrm{y} \leq 260\). This happens when they don't carefully track which variable corresponds to which supplier.

This may lead them to select Choice C (\(0.55\mathrm{x} + 0.15\mathrm{y} \leq 260\))

The Bottom Line:

This problem tests careful translation skills more than complex mathematical reasoning. The key challenge is accurately converting percentages to decimals and maintaining correct associations between suppliers and their respective percentages.